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This is a Quantitative Study study.

September 16, 2025

HyperGraph- and SuperHyperGraph-Based Molecular Models: Weighted, Rough, Neural, and Multipolar Frameworks

Key Points

The study introduces a novel framework that extends molecular graphs to hypergraphs and superhypergraphs, emphasizing varied structures.
Key results reveal that the weighted molecular superhypergraph includes both weighted hypergraphs and unweighted superhypergraphs significantly.
The presented methodologies include examples like methane and acetic acid, showcasing atoms as vertices and bonds as hyperedges effectively.
Diagonal embeddings preserve distances in these new structures, suggesting broad applications in chemical property predictions.

Abstract

We present a unified, set–theoretic framework that extends molecular graphs to hypergraphs and superhypergraphs via iterated power sets. We define Molecular Graphs, Molecular HyperGraphs, and Molecular SuperHyperGraphs, and develop four complements over them: Weighted, Rough, Neural, and Multipolar frameworks. We prove concise inclusion results—most notably, that the Weighted Molecular SuperHyperGraph strictly contains both Weighted Molecular HyperGraphs and (unweighted) Molecular SuperHyperGraphs—while preserving alternating–path distances under canonical embeddings. Compact examples (e.g., methane, ethanol, acetic acid) illustrate how atoms, bonds, functional groups, and higher–order motifs appear as vertices, hyperedges, and superedges under rank constraints. We also provide implementation–agnostic message–passing rules for variable–arity interactions, enabling property prediction and hierarchical analysis in chemistry and chemical biology.

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